5 statistic question

Statistic homework assignment

   

Word-process your answers within this document. Do not create a new file. Show all steps used in arriving at the final answers. Incomplete solutions will receive partial credit.

   

Problem 1

 

The U.S. Census Bureau publishes data on factory orders for all manufacturing, durable goods, and nondurable goods industries. Shown here are factory orders in the United States from 1987 through 1999 ($ billion).

 

(a) Use these data to develop forecasts for the years 1992 through 1999 using a 5-year moving average.

 

(b) Use these data to develop forecasts for the years 1992 through 1999 using a 5-year weighted moving average. Weight the most recent year by 6, the previous year by 4, the year before that by 2, and the other years by 1.

 

(c) Which method is more suitable for forecasting factory orders? Hint: Compare the two methods based on Mean Absolute Deviation (MAD)?

   YearFactory Orders ($ billion)19872,512.719882,739.219892,874.919902,934.119912,865.719922,978.519933,092.419943,356.819953,607.619963,749.319973,952.019983,949.019994,137.0 

(Black, Ken (2006). Business Statistics (4th ed. update). John Wiley & Sons, New York, NY. Page 615)

             

Problem 2

 

The following data list worldwide shipments of personal computers (in thousands) according to Dataquest.

   YearShipments (in thousands)199023,738199126,966199232,411199338,851199447,894199560,171199671,065199782,400199897,321 

(a) Use exponential smoothing to determine the forecast of shipments for the year 1999. Use the actual shipments for 1990 as the starting forecast for 1991. Use a smoothing constant of a = 0.4.

 

(b) Plot the data, fit a trend line, and discuss the strength of prediction of the regression model.

 

(c) Use the regression model to predict the shipments for the year 1999.

 

(d) Compare the two forecasts. Which forecast would you prefer to use and why?

 

(Adapted from: Black, Ken (2006). Business Statistics (4th ed. update). John Wiley & Sons, New York, NY. Page 622)

   

Problem 3

 

Given y = f(x) = x2 + 2x +3

 

a) Use the definitional formula given below to find the derivative of the function.

   

b) Find the value of the derivative at x = 3.

     

Problem 4

 

Given, y = f(x) = 2 x3 – 3×2 + 4x +5

 

a) Use the Power function to find derivative of the function.

 

b) Find the value of the derivative at x = 4.

             

Problem 5

 

The revenue and cost functions for producing and selling quantity x for a certain production facility are given below.

 

R(x) = 16x – x2

 

C(x) = 20 + 4x

 

a) Determine the profit function P(x).

 

b) Use Excel to graph the functions R(x), C(x) and P(x) for the interval 0≤ x ≤ 12. Copy and paste the graph below. Note: Use Scatter plot with smooth lines and markers.

 

c) Determine the average cost at the break-even quantities.

 

d) Determine the marginal revenue R’(x).

 

e) Determine the marginal cost C’(x)

 

f) At what quantity is the profit maximized?